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13 November, 00:10

Michael perez deposited a total of $3000 with two savings institutions. bank a pays interest at the rate of 6%/year, whereas bank b pays interest at the rate of 8%/year. if michael earned a total of $224 in interest during a single year, how much did he deposit in each institution?

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  1. 13 November, 03:19
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    Define

    x = dollars deposited into bank A.

    y = dollars deposited into bank B.

    Then

    x + y = 3000 (1)

    Assume that the compounding interval is monthly, and calculate interest earned.

    Bank A:

    Amount after 1 year is

    A = x (1 + 0.06/12) ¹² = 1.0617x

    Profit = 0.0617x

    Bank B:

    Amount after 1 year is

    A = y (1 + 0.08/12) ¹² = 1.083y

    Profit = 0.083y

    The total profit for 1 year is $224, therefore

    0.0617x + 0.083y = 224 (2)

    From (1), obtain

    y = 3000 - x (3)

    Substitute (3) into (2).

    0.0617x + 0.083 (3000 - x) = 224

    -0.0213x = - 25

    x = 1173.70

    y = 3000 - x = 1826.30

    Answer:

    Michael deposited $1,173.70 into bank A and $1,826.30 into bank B.
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